Sherwood number

2013-11-23T21:50:45Z

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The '''Damköhler numbers''' ('''Da''') are [[dimensionless number]]s used in [[chemical engineering]] to relate the [[chemical reaction]] timescale ([[reaction rate]]) to the [[transport phenomena]] rate occurring in a system. It is named after German chemist [[Gerhard Damköhler]].

In its most commonly used form, the Damköhler number relates the reaction timescale to the [[convection]] times scale, [[flow rate]], through the [[reactor]] for continuous or [[Semibatch reactor|semibatch]] chemical processes:
: <math>\mathrm{Da} = \frac{ \text{reaction rate} }{ \text{convective mass transport rate} }</math>


In reacting systems that include interphase mass transport, the '''second Damköhler number''' ('''DaII''') is defined as the ratio of the chemical reaction rate to the mass transfer rate
: <math>\mathrm{Da}_{\mathrm{II}} = \frac{ \text{reaction rate} }{ \text{diffusive mass transfer rate} }</math>

Since the reaction timescale is determined by the reaction rate, the exact formula for the Damköhler number varies according to the raw law equation. For a general chemical reaction A → B of nth [[Order of reaction|order]], the Damköhler number for a convective flow system is defined as:

: <math>\mathrm{Da} = k C_0^{\ n-1}\tau</math>
where:
* ''k'' = [[chemical kinetics|kinetics]] [[reaction rate constant]]
* ''C''0 = initial concentration
* ''n'' = [[reaction order]]
* <math>\tau</math> = mean [[residence time]] or '''space time'''

On the other hand, the second Damköhler number is defined as:
: <math>\mathrm{Da}_{\mathrm{II}} = \frac{k C_0^{n-1}}{k_g a}</math>
where
* ''kg'' is the global mass transport coefficient
* ''a'' is the interfacial area

The value of Da provides a quick estimate of the degree of [[Conversion (chemistry)|conversion]] that can be achieved. As a [[rule of thumb]], when Da is less than 0.1 a conversion of less than 10% is achieved,and when Da is greater than 10 a conversion of more than 90% is expected.<ref name="Fogler">{{cite book |last=Fogler |first=Scott |title=Elements of Chemical Reaction Engineering |location=Upper Saddle River, NJ |publisher=Pearson Education |year=2006 |edition=4th |isbn=0-13-047394-4 }}</ref>

==References==
{{reflist}}

{{NonDimFluMech}}

{{DEFAULTSORT:Damkohler numbers}}
[[Category:Catalysis]]
[[Category:Chemical engineering]]
[[Category:Dimensionless numbers of chemistry]]
[[Category:Dimensionless numbers of fluid mechanics]]
[[Category:Fluid dynamics]]

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Sherwood number